Parametric vs. Non-Parametric Statistics

• Statistical analysis is the process of collecting and analyzing large data volumes to identify trends and gain valuable insights.
• In experimental research, statistical analysis is used to prove or disprove hypotheses and make predictions about a population.

Parametric vs. Non-Parametric Statistics

• Parametric statistics involve information about the population's distribution being known and based on a fixed set of parameters.
• Nonparametric statistics are used when the information about the population's distribution is unknown
• The parameters are not fixed, necessitating hypothesis testing for the population.

Assumptions for Parametric Tests

• Data needs to be normally distributed, following a bell-shaped curve without skewness.
• Data also needs to have equal variance.
• The data must be continuous.

Parametric & Non-Parametric Tests

• Parametric tests
  • One Sample tests include: t-test and z-test
  • Two Sample tests:
  • Independent Sample consists of: t-test and z-test for two groups.
  • Paired Sample: Paired t-test
• Non-Parametric Tests
  • One Sample tests include: Chi-Square, K-S, Runs test, and Binomial tests
  • Two Sample tests:
    • Independent Sample consists of: Chi-Square, Mann-Whitney, Median, and K-S tests
    • Paired sample includes the Sign, Wilcoxon, McNemar, and Chi-square tests

Choosing Between Parametric and Non-Parametric Tests Based on Data Setup:

• If your data consists of 1 variable with 2 categories between subjects, use the independent t-test for parametric and Mann-Whitney U test for non-parametric analysis.
• For 1 variable with 2 categories within subjects, use the paired t-test (parametric) or Wilcoxon Signed Rank Test (non-parametric).
• When there is 1 variable with more than 2 categories between subjects, perform a One-way ANOVA (parametric) or Kruskal Wallis Test (non-parametric).
• For 1 variable with more than 2 categories within subjects, choose repeated measures ANOVA (parametric) or Friedman's test/Mood's median test (non-parametric).
• In analyzing 1 variable for correlation, perform the Pearson's r (parametric) test or Spearman's p (rho) (non-parametric).

T-Tests

• Used to evaluate the means of one or two populations via hypothesis testing.
• T-tests are applicable when comparing means of two groups.
• Can be one sample, independent, or paired sample T-Tests:

Types of T-Tests

• One Sample: Used with an unknown mean of a group is test against a known mean
• Independent Sample: Used to comparing the means of two different groups
• Paired Sample: Used to comparing means of one group at different times.

One-Sample T-Test

• A statistical hypothesis test used to determine whether an unknown population mean differs from a specific value.
• Formula: t = (x̄ - μ) / (s / √n)
  • x̄ = observed mean of the sample
  • µ = assumed mean
  • s = standard deviation
  • n = sample size

Paired Sample T-Test

• Compares the means of two measurements taken from the same individual, object, or related units.
  • A measurement taken at two different times
  • A measurement taken under two different conditions
  • Measurements taken from two halves or sides of a subject or experimental unit.
• Formula: t = (x̄1 - x̄2) / √(s²(1/n₁ + 1/n₂))

Independent Sample T-Test

• Compares the means of two independent groups to determine if there is statistical evidence that the populations means are significantly different.
• Formula:t = (x̄₁ - x̄₂) / √(s₁²/n₁ + s₂²/n₂)
• x̄₁ = observed mean of 1st sample
• x̄₂ = observed mean of 2nd sample
• s₁ = standard deviation of 1st sample
• s₂ = standard deviation of 2nd sample
• n₁ = sample size of 1st sample
• S₂ = sample size of 2nd sample

P-Value and Alpha Level

• A p-value is used in hypothesis testing to help either back or deny the null hypothesis.
• The smaller the p-value is, the stronger evidence you have to deny the null hypothesis.
• Alpa level, or known as the significance level, signifies the threshold for statistical significance when rejecting the null hypothesis in a statistical test.

T-Value and T-Crit

• A t-value is is tested against a t-critical value to determine a null hypothesis.
• T-value: Value calculated from a sample
• T-critical value: Value obtained from a t-distribution table

Explore the differences between parametric and non-parametric statistical methods. Parametric methods rely on known population distributions and fixed parameters. Non-parametric tests are applied when population distribution information is unavailable. Learn about assumptions for both test types.